It is currently 26 May 2019, 19:49

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# abc is a three-digit number in which a is the hundreds digit

Author Message
TAGS:
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 112

Kudos [?]: 1865 [0], given: 397

abc is a three-digit number in which a is the hundreds digit [#permalink]  12 Aug 2018, 15:52
Expert's post
00:00

Question Stats:

55% (01:36) correct 44% (01:05) wrong based on 27 sessions
abc is a three-digit number in which a is the hundreds digit, b is the tens digit, and c is the units digit. Let $$&(abc)& = (2^a)(3^b)(5^c)$$. For example, $$&(203)& = (2^2)(3^0)(5^3) = 500$$. For how many three-digit numbers abc does the function &(abc)& yield a prime number?

(A) Zero
(B) One
(C) Two
(D) Three
(E) Nine
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 112

Kudos [?]: 1865 [1] , given: 397

Re: abc is a three-digit number in which a is the hundreds digit [#permalink]  17 Aug 2018, 16:33
1
KUDOS
Expert's post
Explanation

Since a prime number has only two factors, 1 and itself, $$(2^a)(3^b)(5^c)$$ cannot be prime unless the digits a, b, and c are such that two of the digits are 0 and the third is 1.

For instance, $$(2^0)(3^1)(5^0) = (1)(3)(1) = 3$$ is prime.

Thus, the only three values of abc that would result in a prime number & (abc)& are 100, 010, and 001. However, only one of those three numbers (100) is a three-digit number.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Manager
Joined: 02 Dec 2018
Posts: 74
Followers: 0

Kudos [?]: 7 [0], given: 60

Re: abc is a three-digit number in which a is the hundreds digit [#permalink]  02 Dec 2018, 08:50
Edit: Nevermind, silly mistake.

Last edited by QuantumWonder on 04 Dec 2018, 18:54, edited 2 times in total.
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 111 [0], given: 4

Re: abc is a three-digit number in which a is the hundreds digit [#permalink]  02 Dec 2018, 19:33
Expert's post
QuantumWonder wrote:
I am really confused. The function &abc& being 1,0,0 yields &100&=2^2*3^0*5^0 = 4. 4 is not a prime number. What am I misinterpreting?

hi
&abc& = $$2^a3^b5^c$$..
so here &abc& = &100&= $$2^13^05^0=2$$ and 2 is prime..
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: abc is a three-digit number in which a is the hundreds digit   [#permalink] 02 Dec 2018, 19:33
Display posts from previous: Sort by